Get a result set flagging where there is a history going back 3 months

I have a table called Addresses that stores address history for our members like this:

I want to create a results set where there is a flag column if the member has been at the same address 3 consecutive months or more, with one row per member like this:

Only member 5555555 has been at the same address in the past 3 consecutive months. Member 7777777 has been at the same address but not for the past 3 consecutive months, there is gaps in their enrollment history.

I tried using ROW_NUMBER like:

with cte as (
SELECT MEDICAID_ID, FILE_MONTH,RES_ADDRESS_1, 
RES_CITY, 
ROW_NUMBER() OVER (PARTITION BY ID,ADDRESS ORDER BY ID, ADDRESS) as RN
FROM Addresses
WHERE FILE_MONTH > '202412'
)

SELECT MEDICAID_ID, CASE WHEN RN >= 3 THEN 'Y' ELSE 'N' END AS SAME_ADDRESS_3_MONTHS
FROM cte

But I get rows where SAME_ADDRESS_3_MONTHS is N even when they have been there the past 3 months and I get multiple rows per member. Im not sure how to get this.

I think you can solve your issue with a query that uses a CTE and Row_Number(). The final query needs to group by ID and check the Max(RN).

WITH CTE as
(
SELECT ID,  Address, 
  ROW_NUMBER() OVER (PARTITION BY ID,ADDRESS ORDER BY ID, ADDRESS) as RN
FROM Addresses
WHERE   FILE_MONTH > 202412
)
SELECT ID, CASE WHEN Max(RN) >2 THEN 'Y' ELSE 'N' END as SAME_ADDRESS_3_MONTHS
FROM CTE
GROUP BY ID

fiddle